I'm only talking about weapon hitmarkers and I don't see how knowing when your shots hit is too much information at all. You should know which shots hit and which missed, that's the whole point of shield flare. Hit markers are just more visible. Shooting is less frustrating and more satisfying when you know your shots are hitting.
I literally don't see a single negative with weapon hitmarkers.
So here's the thing: a designer wants to give the player enough information that the player can complete their goal, but the designer wants to keep enough information from the player so that it isn't a cakewalk. I'll ignore PvE entirely, as I know the crux of this argument is in the PvP side. When it comes to one player shooting at another, the most important thing at a very basic level is whether or not they got a hit or a miss.
Now what tools can a designer utilize to let the player know that they have a hit or a miss? They could have a number pop up showing how much damage was dealt. With a health bar, this is huge. This lets the player know not only how much damage was dealt in raw numbers, but also essentially how much more they have to deal. Even without a health bar, it's giving players incredibly detailed information about what they've just done. I'm just going to toss this one aside right away. There's no challenge in learning, and when a shot misses, it doesn't feel as big of a deal, because another number will pop up on the next hit. (A good look at this is in Destiny. Engagements don't feel as big of a deal in part because of the feedback system.)
Let's abstract that concept just a bit and say there's a hit marker. This adds a bit of challenge to learning, as you are forced to learn how many hits will net a kill. Strangely enough, misses feel like a bigger deal than they did with numbers. The big problem lies in the moment to moment decision making that hit markers give. In a simple retreat encounter, Player A tries to disengage from Player B. Player B has counted 9 BR hit markers on Player A. In a situation with hit markers Player B knows that from just those 9 hit markers, that it's more than likely a good idea to immediately follow up on the attack. What has Player B learned from that encounter aside from counting hit markers?
Let's take a look at no UI elements signalling hits, and just at in-game visual and audio effects, while also using the Player A/B scenario from before. In this scenario, Player B has to learn how much damage they've dealt in correspondence with how intense the effect is on their screen. There's a higher level of learning and still misses feel like a big deal. Moment to moment decision making is based more on previous learning than on counting a UI element.
Now when would having hit markers be more valuable than not? It's primarily in debugging what isn't working. The best example is in Halo 3. Inconsistent networking conditions could cause sniper shots to be blood shots. With hit markers, the game would respond by not showing a hit marker, because it didn't fully register. Without them, players tended to waste multiple shots. But take note that under normal conditions, this wouldn't be an issue. So now a big question to the designer should be "When do I allow players to see if things are in an abnormal condition?" With hit markers enabled, the answer is always. Like I said before, the problem is that it lessens the challenge in learning the game.
I think it'd be an interesting experiment to have players that have a high ping to the server give hit markers when they are hit, while other players don't. It isn't the best solution, but I think it could be interesting. If I were the designer in question, I would only use them as a post game tool in Theater. This allows players to go back in and see what went wrong on certain engagements. Ideally, using Focused settings would allow players to avoid abnormal networking conditions altogether(but we all know that isn't the case in reality). In all honesty, I don't see hit markers going anywhere; I think it's as ingrained in 343's Halo as Sprint. I would love for the game to go back to as good of a feedback system as Reach had.